1. Field of the Invention
The present invention relates to systems and methods for magnetic resonance imaging (MRI). More particularly, the present invention relates to systems and methods for MRI spatial encoding and image reconstruction.
2. Description of the Prior Art
MRI uses the nuclear magnetic resonance (NMR) phenomenon to produce images. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the nuclei in the tissue attempt to align with this polarizing field, and precess about it at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a radio frequency (RF) magnetic field (excitation field B1) that is in the x-y plane and that is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped,” into the x-y plane to produce a net transverse magnetic moment Mxy. A signal is emitted by the excited nuclei or “spins”, after the excitation field B1 is terminated, and this signal may be received and further processed to form, or to reconstruct, an image.
Conventional MRI employs temporally and spatially variable magnetic fields to encode the position by the local Larmor frequency of spins. To this end, the gradient systems applied for MRI are designed to produce spatially linearly varying fields (i.e. constant gradients) in three orthogonal directions x, y, z, which lead to a direct mapping of the local resonance frequencies to spatial coordinates. Through the constant gradients, images of the substance, or human tissue, without distortions may be produced after Fourier transformation of the time domain signals. Constant gradients are advantageous in the constant voxel size, and in that the signal intensities across the image can be directly compared without the need for any volumetric correction. The use of constant gradients to encode the physical parameter also allows for isotropic parameter encoding.
By switching orthogonal linear gradients, the localization of magnetic resonance (MR) signals is commonly achieved to obtain a bijective mapping between the magnetization precession frequencies and spatial locations. Specifically, the incremental gradient moment (time integral of the gradient strength) between consecutive data samples and the maximal gradient moment respectively corresponds to the field-of-view (FOV) and the spatial resolution based on the Nyquist sampling theorem. This imaging principle is applied for mapping, for example, a three dimensional object, onto a three dimensional k-space, each sample of which measures the projection of the object to be imaged onto one specific three-dimensional spatial harmonic function. Spatial encoding using orthogonal linear gradients is advantageous in that the images can be reconstructed efficiently and uniquely using the fast Fourier transformation when acquired data satisfy the Nyquist sampling theorem and the data locate on evenly separated Cartesian grids.
Instead of using linear gradients, nonlinear gradients are used to improve the dynamic range of MR signals and to localize NMR signals without using selective excitation. Recently, it has been suggested that parallel imaging technique using localized gradients (PatLoc) can achieve high spatial resolution images and reduce the peripheral nerve stimulation hazard by using nonlinear surface gradient elements and an RF receiver array. O-space imaging is suggested to be a different imaging approach using the Z2 magnetic field gradient together with the x- and y-gradients to make the high resolution accelerated images. The use of nonlinear imaging gradients, however, makes the images have anisotropic spatial resolution and makes the image reconstruction become more complicated.
It is desired to develop a new approach for encoding the object and for reconstructing the image thereof with an MRI system to improve the reconstruction resolution and to save the time necessary for the same.